Problem 20 - Campbell Biology Concepts & Connections

Question

Red blood cells, which carry oxygen to body tissues, live for only about 120 days. Replacement cells are produced by cell division in bone marrow. How many cell divisions must occur each second in your bone marrow just to replace red blood cells? Here is some information to use in calculating your answer: There are about 5 million red blood cells per cubic millimeter \(\left(\mathrm{mm}^{3}\right)\) of blood. An average adult has about \(5 \mathrm{~L}\left(5,000 \mathrm{~cm}^{3}\right)\) of blood. (Hint: What is the total number of red blood cells in the body? What fraction of them must be replaced each day if all are replaced in 120 days?)

Step-by-Step Solution

Answer

About 2.41 million red blood cells must be replaced per second.

Step 1 - Calculate the total number of red blood cells

First, find out the total number of red blood cells in the body. There are 5 million red blood cells per cubic millimeter of blood. Since 1 cm^3 = 1000 mm^3, an average adult has about 5,000,000 mm^3 of blood. Therefore, total red blood cells = 5,000,000 cells/mm^3 * 5,000,000 mm^3.

Step 2 - Perform the multiplication

Multiply the number of red blood cells per cubic millimeter by the total volume in cubic millimeters: Total red blood cells = 5,000,000 cells/mm^3 * 5,000,000 mm^3 = 2.5 × 10^{13} red blood cells.

Step 3 - Calculate the daily replacement fraction of red blood cells

Given that red blood cells live for 120 days, the fraction of them that must be replaced each day is 1/120. Fraction to replace per day = 2.5 × 10^{13} / 120.

Step 4 - Perform the division

Divide to find the number of red blood cells that must be replaced each day: Number of red blood cells to replace per day = 2.5 × 10^{13} / 120 ≈ 2.083 × 10^{11}.

Step 5 - Calculate the replacement rate per second

There are 86400 seconds in a day (24 hours/day * 60 minutes/hour * 60 seconds/minute). Therefore, the number of red blood cells that must be replaced per second is found by dividing the daily replacement requirement by the number of seconds in a day: Number of red blood cells to replace per second = 2.083 × 10^{11} / 86400.

Step 6 - Perform the final division

Divide to find the number of red blood cells that must be replaced each second: Number of red blood cells to replace per second = 2.083 × 10^{11} / 86400 ≈ 2.41 × 10^6 red blood cells per second.

Key Concepts

Cell Division

Cell division is a fundamental biological process where a single cell splits into two identical daughter cells. This process ensures the growth, repair, and reproduction of organisms. In the context of red blood cell turnover, cell division occurs in the bone marrow, a critical site for generating new red blood cells to replace the old ones. There are two main types of cell division: mitosis and meiosis. For red blood cells, the relevant process is mitosis, which results in two genetically identical cells. Properly functioning mitosis is essential for maintaining the body's supply of oxygenated blood.

Human Physiology

Human physiology is the study of how the human body functions. This includes understanding various systems and how they work together. The circulatory system, especially the production and lifecycle of red blood cells, is a vital aspect. Red blood cells are responsible for carrying oxygen from the lungs to tissues and returning carbon dioxide for exhalation.
Understanding the lifecycle of red blood cells, including their turnover and replacement, is crucial. They typically live for around 120 days before they are broken down and replaced, which ties into the body's need to continually produce new cells to maintain efficient oxygen transport.

Mathematical Biology

Mathematical biology involves using mathematical models to understand biological processes. Calculating red blood cell turnover is an excellent example of this application. Using the given formula and numbers, we can determine the rate at which red blood cells need to be produced.
For example, by knowing the total number of red blood cells and their lifespan, we can calculate how many need to be replaced each day. With the help of division and multiplication, we determine the exact number of cells produced per second, which in this case is approximately \(2.41 \times 10^6\) cells per second. This mathematical approach helps us understand and visualize the biological processes at play.

Bone Marrow Function

Bone marrow is a spongy tissue found in bones, and it plays a vital role in producing blood cells, including red blood cells. Within the bone marrow, stem cells divide and differentiate into various types of blood cells. Proper bone marrow function is essential for producing the millions of new red blood cells needed daily to replace the ones that have aged and been filtered out by the spleen and liver.
The turnover rate calculated indicates the remarkable efficiency and capacity of the bone marrow. On average, it needs to produce about \(2.41 \times 10^6\) red blood cells per second to maintain adequate oxygen levels in the body.

Hematology

Hematology is the study of blood, blood-forming organs, and blood diseases. A significant area of this field focuses on understanding red blood cells, their production, and their role in health and disease. Hematologists examine how red blood cells are created in the bone marrow, their lifecycle, and their function in transporting oxygen and carbon dioxide.
They also study various disorders that affect red blood cells, such as anemia and polycythemia. Understanding the turnover rate of red blood cells can help in diagnosing and treating these conditions more effectively, ensuring that the body's circulatory system functions optimally.